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GCSE Mathematics · key term
Perpendicular lines meet at a right angle. Where both gradients are defined and non-zero, their gradients multiply to .
Used by AQA, Edexcel and OCR
Specification A16 · Paper 1, Paper 2, Paper 3
Revise: Circle EquationsThe radius drawn from the centre to that point of contact is perpendicular to the tangent. Thus the circle tells us the direction of the radius, and perpendicular gradients then tell us the direction of the tangent.
Specification A16 · Paper 1, Paper 2, Paper 3
Perpendicular lines meet at a right angle. Where their gradients are defined and non-zero, the gradients multiply to .
Revise: Circle EquationsThese form the perpendicular sides of a right-angled triangle whose hypotenuse is the radius.
Specification 8.02a, 8.05e, 8.05f · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
A line that crosses another line at a right angle of .
Revise: BisectorsA perpendicular line that crosses somewhere other than the midpoint is not a bisector.
Meeting at a right angle of .
Lines that meet at a right angle of 90°.
Do not use the radius gradient as the tangent gradient. The radius and tangent are perpendicular, so their gradients are negative reciprocals when both gradients are defined.
Do not assume that bisecting a segment automatically gives a perpendicular line; your completed construction must do both.
Check that the line passes through the centre before using this theorem. A line being perpendicular to a chord is not enough on its own.
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